HAL will be down for maintenance from Friday, June 10 at 4pm through Monday, June 13 at 9am. More information
Skip to Main content Skip to Navigation
Conference papers

Minkowski Sum of Ellipsoids and Means of Covariance Matrices

Abstract : The Minkowski sum and difference of two ellipsoidal sets are in general not ellipsoidal. However, in many applications, it is required to compute the ellipsoidal set which approximates the Minkowski operations in a certain sense. In this study, an approach based on the so-called ellipsoidal calculus, which provides parameterized families of external and internal ellipsoids that tightly approximate the Minkowski sum and difference of ellipsoids, is considered. Approximations are tight along a direction l in the sense that the support functions on l of the ellipsoids are equal to the support function on l of the sum and difference. External (resp. internal) support function-based approximation can be then selected according to minimal (resp. maximal) measures of volume or trace of the corresponding ellipsoid. The connection between the volume-based approximations to the Minkowski sum and difference of two positive definite matrices and their mean using their Euclidean or Riemannian geometries is developed, which is also related to their Bures-Wasserstein mean.
Complete list of metadata

Cited literature [5 references]  Display  Hide  Download

https://hal.archives-ouvertes.fr/hal-02436451
Contributor : Jesus Angulo Connect in order to contact the contributor
Submitted on : Monday, January 13, 2020 - 9:45:35 AM
Last modification on : Wednesday, November 17, 2021 - 12:27:17 PM
Long-term archiving on: : Tuesday, April 14, 2020 - 2:17:44 PM

File

30-Angulo.pdf
Files produced by the author(s)

Identifiers

Citation

Jesus Angulo. Minkowski Sum of Ellipsoids and Means of Covariance Matrices. International Conference on Geometric Science of Information GSI 2019, Aug 2019, Toulouse, France. pp.107-115, ⟨10.1007/978-3-030-26980-7_12⟩. ⟨hal-02436451⟩

Share

Metrics

Record views

2603

Files downloads

371